[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2005.42.3.591

SOME NEW RESULTS RELATED TO BESSEL AND GRUSS INEQUALITIES IN 2-INNER PRODUCT SPACES AND APPLICATIONS

DRAGOMIR S.S. (SCHOOL OF COMPUTER SCIENCE AND MATHEMATICS)
CHO, Y.J. (DEPARTMENT OF MATHMATHICS, GYEONGSANG NATIONAL UNIVERSITY)
KIM, S.S. (DEPARTMENT OF MATHMATHICS, DONGEUI UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.42, no.3, 2005 , pp. 591-608 More about this Journal

Abstract

Some new reverses of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces are pointed out. Applications for some Gruss type inequalities and for determinantal integral inequalities are given as well.

Keywords

Bessel's inequality; Gruss' inequality; 2-inner product; Lebesgue integral; synchronous functions;

Citations & Related Records

Reference

1	Y. J. Cho, Paul C. S. Lin, S. S. Kim, and A. Misiak, Theory of 2-inner product spaces, Nova Science Publishers, Inc., New York, 2001
2	Y. J. Cho, M. Matic, and J. E. Pecaric, On Gram's determinant in 2-inner product spaces, J. Korean Math. Soc. 38 (2001), no. 6, 1125-1156
3	S. S. Dragomir, Y. J. Cho, S. S. Kim, and Y.-H. Kim, On Bessel's and Gruss' inequalities for orthonormal families in 2-inner product spaces and applications, Preprint on line: http://www.mathpreprints.com/math/Preprint/Sever/20030929/1/
4	S. S. Dragomir, Y. J. Cho, S. S. Kim, and J. Roumeliotis, A reverse of Bessel's inequality in 2-inner product spaces and some Gruss type related results with applications, preprint on line: http://www.mathpreprints.com/math/Preprint/Sever/20030923.1/2
5	R. W. Freese and Y. J. Cho, Geometry of linear 2-normed spaces, Nova Science Publishers, Inc., New York, 2001